"shadowy conspiracy" is correct and usable in written English.
You can use it to refer to a secret plan by a group of people that is not fully understood. For example, "Many people believed there was a shadowy conspiracy behind the politician's sudden resignation."
NBC has Blindspot, a sort of procedural where deciphering a woman's tattoos gets us closer to some shadowy conspiracy.
The filmmakers didn't have to invent a shadowy conspiracy—"Grande Fratello" has been on the air since 2000.
Now the trailer's bound to kick up a gear – perhaps she'll uncover a shadowy conspiracy of brutality and close-up violence.
If I'd had to guess who was leading the shadowy conspiracy against me, I pretty much would have gone for IT.
It's a shadowy conspiracy that has existed since the dawn of time, secretly pulling the strings of every major organisation in the world.
The film aims to scare Americans into thinking that the United States is under attack from a shadowy conspiracy of Muslim groups that, it claims, pretend to be part of mainstream society while plotting its downfall.
"The New World Order," with its shadowy conspiracies hatched by the Council on Foreign Relations and the Trilateral Commission.
But the core issue before the attack was a lack of resources and skilled management, not shadowy conspiracies.
As someone who has always complained of shadowy conspiracies, Perot can now rail against a visible group that has wronged him.
Anyone weaned on the shadowy conspiracies of film noir will shrug at the plot of "Renaissance," but the lack of novelty is deliberate; it is the shadows themselves that have changed.
The A.V. Club Zack Handlen felt that the third season's focus on a villainous Group reduced them to "yet another cabal with seemingly limitless influence and power", describing them as "just another one of Carter's beloved shadowy conspiracies".
